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%I #12 Feb 26 2018 19:21:59
%S 1,2,2,3,3,3,3,6,4,4,3,4,12,5,5,6,5,5,24,6,6,7,12,6,6,48,7,7,3,9,24,7,
%T 7,96,8,8,9,5,14,48,9,8,192,9,9,3,18,6,18,96,10,9,384,10,10,7,6,36,7,
%U 28,192,11,10,768,11,11,12,9,7,72,8,36,384,12,11
%N Square array T(n, k) read by antidiagonals upwards, n > 0 and k > 0: T(n, k) is the k-th positive number whose Collatz sequence contains n.
%C The n-th row corresponds to indices of rows in A070165 containing n.
%H Rémy Sigrist, <a href="/A299962/a299962.gp.txt">PARI program for A299962</a>
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F T(n, 1) = A070167(n) for any n > 0.
%F T(3*n, k) = 3*n * 2^(k-1) for any n > 0 and k > 0.
%F If the Collatz conjecture is true, then:
%F - T(1, k) = k for any k > 0,
%F - T(2, k) = k+1 for any k > 0.
%e Array T(n, k) begins:
%e n\k| 1 2 3 4 5 6 7 8 9 10
%e ---+---------------------------------------------------------
%e 1| 1 2 3 4 5 6 7 8 9 10 --> A000027 ?
%e 2| 2 3 4 5 6 7 8 9 10 11
%e 3| 3 6 12 24 48 96 192 384 768 1536 --> A007283
%e 4| 3 4 5 6 7 8 9 10 11 12
%e 5| 3 5 6 7 9 10 11 12 13 14
%e 6| 6 12 24 48 96 192 384 768 1536 3072 --> A091629
%e 7| 7 9 14 18 28 36 37 43 49 56
%e 8| 3 5 6 7 8 9 10 11 12 13
%e 9| 9 18 36 72 144 288 576 1152 2304 4608
%e 10| 3 6 7 9 10 11 12 13 14 15
%o (PARI) See Links section.
%Y Cf. A000027, A007283, A091629, A070165, A070167.
%K nonn,tabl
%O 1,2
%A _Rémy Sigrist_, Feb 22 2018
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